Wednesday, September 24th, 2014
3:30pm - 4:30pm, in Science 2-066

Hiro Tanaka

Harvard University

Invariants of modules and algebras as invariants of stratified spaces

Abstract: Factorization homology is a way of constructing invariants of algebras, and of manifolds, at the same time. For instance, to an associative algebra and a circle, one associates the Hochschild homology of the algebra. These invariants are more sensitive to the manifold's diffeomorphism class than usual homology (which is only sensitive to the manifold up to homotopy equivalence). Moreover, the invariants satisfy a local-to-global property similar to excision for homology. We'll talk about how this can be generalized to include algebras with modules (and manifolds with stratifications) to create, for instance, link invariants. This is joint work with David Ayala and John Francis.